Medical consultation is available In the Erstaufnahme (initial reception, EA). You will receive free medical treatment there and get a referral, if necessary.Asylum applicants in Hamburg are insured by the AOK Bremen/Bremerhaven. You do not need to register yourself, the EA will take care of it.
In the EA, you will receive a “certificate for presentation to the attending physician” and later an electronic health card (eGK). You can go to the doctor with the certificate or the health card. Treatment is generally free.